Letter pubs.acs.org/NanoLett
Single-Fluxon Controlled Resistance Switching in Centimeter-Long Superconducting Gallium−Indium Eutectic Nanowires Weiwei Zhao,*,†,‡ Jesse L. Bischof,†,¶ Jimmy Hutasoit,†,‡ Xin Liu,†,‡ Thomas C. Fitzgibbons,†,¶ John R. Hayes,§ Pier J.A. Sazio,§ Chaoxing Liu,†,‡ Jainendra K. Jain,†,‡ John V. Badding,†,¶ and M. H. W. Chan*,†,‡ †
Center for Nanoscale Science, Pennsylvania State University, University Park, Pennsylvania16802, United States Department of Physics, Pennsylvania State University, University Park, Pennsylvania16802, United States ¶ Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania16802, United States § Optoelectronics Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, U.K. ‡
S Supporting Information *
ABSTRACT: The ability to manipulate a single quantum object, such as a single electron or a single spin, to induce a change in a macroscopic observable lies at the heart of nanodevices of the future. We report an experiment wherein a single superconducting flux quantum, or a fluxon, can be exploited to switch the resistance of a nanowire between two discrete values. The experimental geometry consists of centimeter-long nanowires of superconducting Ga−In eutectic, with spontaneously formed Ga nanodroplets along the length of the nanowire. The nonzero resistance occurs when a Ga nanodroplet traps one or more superconducting fluxons, thereby driving a Josephson weak-link created by a second nearby Ga nanodroplet normal. The fluxons can be inserted or flipped by careful manipulation of the magnetic field or temperature to produce one of many metastable states of the system. KEYWORDS: GaIn, eutectic, superconducting nanowire, single flux quantum, resistance switching
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typical length of 20 cm. The liquid metal wires stay inside the fiber even after the pressure is removed. The inner diameter of these fibers is uniform to a few nanometers along the entire length as measured by cross sectional scanning electron micrograph. They have a surface roughness on the order of ±0.1 nm RMS.16,17 After the infiltration, both ends of a 6 mm segment of the fiber were immersed into ∼1 mm diameter reservoirs of Ga or Ga−In and then electrically connected by 100 μm diameter Au wires for four leads transport measurements (Figure 1c). As shown in Figure 1d, a pure Ga wire shows a superconducting transition at 1.1 K, same as the bulk value.18 The room temperature resistivity value of pure Ga wire is 1.6 times the bulk value. This indicates that the nanowires inside the glass fiber are of higher quality than those fabricated by ebeam assisted evaporation and also those grown by electrodeposition in track-etched membrane. Ga−In nanowires with Ga concentration slightly higher than the eutectic point (75% Ga by weight) show two resistance steps (Figure 1e), the first from 11 kΩ to 60 Ω between 3.5 and 5 K and the second to zero resistance more sharply at 1.1 K. This can be understood
odern techniques have made it possible to observe a dramatic modulation of resistance induced by the addition of a single electron into a quantum dot, such as a single electron transistor.1−6 Recent experiments have shown that it is also possible to detect electrical signatures due to a change in the state of a single electron spin in a variety of physical systems.7−11 Single flux quantum sensitivity has also been observed in superconducting loop devices based on Josephson junctions.12,13 However, the size of the unit based on this structure is still larger than tens of micrometer.14 We report here on switching between a superconducting and a resistive state by the addition of a single magnetic flux quantum in sub150 nm geometry. This is made possible by the availability of centimeter-long superconducting Ga−In nanowires with multiple Ga nanodroplets residing along the length. This “peas in a pod” configuration of two superconducting materials with different transition temperatures and critical fields is crucial for this purpose; the normal Ga nanodroplets surrounded by superconducting Ga−In alloy in 150 nm diameter wire are natural locations where fluxons can be trapped. “Peas in a Pod” Configuration of the GaIn Nanowires. The nanowires studied in this experiment were fabricated by means of modified high pressure infiltration15 (Supporting Information, Figure S1) of molten liquid Ga or Ga−In into hollow silica fiber of 150 nm inner diameter (Figure 1a,b) and © 2014 American Chemical Society
Received: August 26, 2014 Revised: November 3, 2014 Published: November 26, 2014 153
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Figure 1. Ga and Ga−In nanowires of 150 nm diameter and 6 mm length. (a) An optical image of the glass fiber infiltrated with Ga. (b) An end view of a hollow fiber by field emission scanning electron microscopy. (c) The schematic for four probe transport measurements. (d) Resistance as a function of temperature (R vs T) at zero field of a pure Ga nanowire showing a superconducting transition at 1.1 K, the bulk Tc value. The room temperature resistivity is 45.3 μΩ·cm, 1.6 times the bulk value. The inset shows a warming−cooling hysteresis loop, indicating that Ga inside the fiber freezes at 250 K instead of 303 K, the bulk freezing point. (e) R vs T at zero field for a Ga−In nanowire with Ga concentration slightly above the eutectic concentration (75% Ga by weight). A two stage superconducting transition at 3.5−5 and 1.1 K is found. Warming and cooling hysteresis similar to that of pure Ga is also found. (f) A two-dimensional X-ray fluorescence map at 190 K of the Ga−In nanowire, showing two droplets in close proximity with high Ga concentration surrounded by Ga−In eutectic (EGaIn). The spatial resolution is 25 nm. The excitation current used here, unless specified otherwise, is 5 nA.
Figure 2. Voltage−current (V−I) scans for the Ga−In nanowire. (a) V vs I under different H at T = 0.5 K. (b) V vs I at different T under zero field. V−I measurements show many steps in V. The steps are signatures of critical currents in the nanowire. These different critical currents indicate that there are multiple Ga droplets of different diameters and hence different thicknesses of the surrounding Ga−In eutectic shell or weak links in the nanowire.
Figure 3. Magnetoresistance of the Ga−In nanowire. (a) The magnetoresistance results are qualitatively different below and above Tc = 1.1 K. At T = 1.2 K, the magnetoresistance results show that resistance (R) stays constant at 60 Ω at low field and increases with magnetic field (H) for H > 500 Oe, which plateaus to the normal state value of 11 kΩ. The magnetoresistance at 0.5 K shows a two-step transition. A sharp transition occurs at a specific value 490 Oe, which we designated as Hc1, and then there is a gradual increase in resistance toward the normal state value with increasing magnetic field. There is no well-defined critical field for the second transition. For specificity, we choose Hc2 as the field value where resistance of the nanowire is 90% of the normal state value. Between Hc1 and Hc2 the EGaIn is in the mixed state. (b) Hc2 as a function of temperature (T). Beyond Hc2(T), the EGaIn is normal.
in terms of phase separation into two regions;19,20 one is pure Ga with a lower superconducting transition (Tc) at 1.1 K, and the other is Ga−In eutectic (EGaIn) with a higher superconducting transition (Tc′) between 3.5 and 5 K. We have directly confirmed that the phase separated residual Ga forms nanodroplets surrounded by EGaIn by X-ray fluorescence (XRF) spectroscopy21 (Figure 1f). The Ga nanodroplets are likely to be of different sizes, residing randomly along the nanowire like peas in a pod. If all Ga nanodroplets were very small, the resistance of the nanowire would remain zero so long as EGaIn is superconducting, independent of whether the Ga nanodroplets are normal or superconducting. We assign the 60 Ω resistance to a relatively large normal Ga nanodroplet with very thin EGaIn layer, which is driven normal by the excitation current of 5 nA. This assignment is confirmed by voltage− current measurements (Figure 2) that show many steps in
voltage with increasing current suggesting the presence of multiple Ga nanodroplets with different diameters and surrounded by EGaIn shells of different thicknesses with different critical currents,22 which range from nanoamps to tens of microamps in this work. The critical magnetic fields at which vortices can tunnel through the EGaIn shells also depend on the thickness of the EGaIn shells for a fixed excitation current; this is confirmed by R vs H scanning at fixed current (Supporting Information, Figure S2). 154
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Figure 4. Resistance (R) as a function of magnetic field (H) and temperature (T) for the Ga−In nanowire, obtained by two different scan paths of R vs H at fixed T and R vs T at fixed H. All measurement scans began by cooling the sample from 8 K under zero H to 0.5 K. (a−c) Magnetoresistance measurements with the field perpendicular to the nanowire at 0.5, 1.0, and 1.2 K. (d) R vs T scans at 0 Oe. (e, f) R vs T scans under 200 Oe when the maximum temperature is 2 K (e) and 8 K (f). (g) Three dimensional (3D) R(T,H) by H scanning at fixed T. (h) 3D R(T,H) by T scanning at fixed H. The warming−cooling process starts from 0.5 K, warms to 8 K, and cools to 0.5 K.
The same Tc is found when the wire is cooled under zero field (Figure 4d) irrespective of the maximum temperature reached in the warming cycle. Similarly, no hysteresis is seen in cycle under 200 Oe if the maximum temperature is 2 K (Figure 4e). However, if the maximum temperature is increased to 8 K in the cycle, then Tc is suppressed to 0.8 K during cooling when placed under the same 200 Oe (Figure 4f). A more complete view of the hysteretic behaviors as a function of H and T plots is shown in Figure 4g,h, respectively. Figure 5 summarizes the hysteretic behavior in both H and T scans. No hysteretic behavior is seen if the measurement path, such as paths a and d, is kept inside of the black solid line, which is Hc1(T) of EGaIn, the phase boundary separating the Meissner state and the mixed state. We define this zero resistance state obtained at the end of paths a or d as state A. Hysteretic behaviors happen when the black line is crossed during the measurement, paths b and c. Although both paths b and c end at the same low field and low temperature region, different resistance, namely, zero and 60 Ω, respectively, are found. This indicates that these paths lead to different final states B and C.
Hysteretic Resistance Switching Behaviors. The qualitative difference in the magnetoresistance below and above Tc = 1.1 K is striking (Figure 3). When the temperature (T) is 1.2 K, the magnetoresistance stays constant at 60 Ω at low fields and increases with magnetic field (H) for H > 500 Oe, which plateaus to the normal state value of 11 kΩ near 2800 Oe, which we will call Hc2. Beyond Hc2, the GaIn wire becomes normal. The magnetoresistance below 1.1 K (Figure 4a,b) shows hysteretic switching between zero and 60 Ω. When H is increased to a specific value, which we designate as Hc1, the resistance (R) abruptly jumps from zero to 60 Ω and stays at this value even when H is reverted to zero. When H reaches a negative specific field (−Hc1′) (|Hc1′| < |Hc1|), R drops back to zero. R jumps to 60 Ω again when H reaches −Hc1. After H reverts to positive direction, R will follow a symmetric loop. At T = 1.2 K > Tc, no hysteresis shows up in the magnetoresistance results (Figure 4c). Hysteretic behavior was also seen in R vs T scans when the wire was subjected to warming− cooling cycles at fixed H provided the maximum temperature exceeded a certain value. During the warming process, the superconducting transition (to 60 Ω) is found at 1.1 K for all field values below 330 Oe (Supporting Information, Figure S3). 155
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Fluxon Trapping Model. The hysteretic resistance switching behaviors and the three different history dependent states can be understood by a fluxon trapping model. As noted above, normal Ga nanodroplets are natural locations where fluxons can be trapped. In particular, once a fluxon going through a relatively small Ga nanodroplet is trapped, it cannot leak out so long as the surrounding EGaIn is superconducting. However, trapped fluxons cannot cause any resistance. The simplest model that can exhibit both trapped fluxons and a nonzero resistance is that of two Ga nanodroplets of different sizes in close proximity, as shown in Figure 6. We identify the states A, B, and C as the states with zero, one, and two fluxons trapped in the smaller Ga nanodroplet, respectively. The thin EGaIn layer surrounding the larger nanodroplet behaves like a weak link not capable of capturing a fluxon, and the 60 Ω resistance appears when the larger Ga nanodroplet becomes normal. This is the case when the temperature is raised above the orange line in path a in Figure 5. The orange line is independent of external field at 1.1 K because the Ga droplets “see” zero field due to the Meissner effect of the GaIn shell. The Meissner effect also assures that no fluxon is captured by the smaller Ga nanodroplet. Along path “b”, when the black line is crossed from high to low temperatures, a single fluxon is trapped by the smaller Ga nanodroplet. As a result of the magnetic field due to the circulating currents supporting this fluxon, it is necessary to go to a lower T (green line in Figure 5) before the nearby larger Ga nanodroplet becomes superconducting (The green line separates the superconducting and normal phases of the larger Ga nanodroplet in the presence of the magnetic field due to a single trapped fluxon in the smaller nanodroplet and the external field). Finally, along the path c, when the black line is crossed at a much higher magnetic field than that in the path b, two fluxons are trapped in the smaller nanodroplet. The circulating current is now so large that it drives the larger nanodroplet normal even at a zero external H and the lowest T (0.5 K in our study). This explains how a state with nonzero resistance can be stable even under a zero external H (state C): the stability comes from the trapping of fluxons in the smaller Ga nanodroplet while the resistance comes from the larger one. We note that the number of trapped fluxons depends on the external H; we have schematically depicted the regions that trap zero, one, and two fluxons by dashed lines in the phase diagram of Figure 5. This model is qualitatively consistent with all the observations. It is not possible to make the model quantitative, given the lack of detailed and precise information about the configuration of the Ga nanodroplet pair. However, semiquantitative statements can be made regarding the plausibility of the above model of fluxon trapping. According to the XRF results, the Ga nanodroplets are of elliptical shape with dimensions ranging from tens to hundreds of nanometers. It is reasonable to infer that when the long axis of the larger elliptical Ga nanodroplet reaches ∼300 nm, its width would be close to 150 nm, the diameter of the nanowire, with the surrounding EGaIn shell forming a weak link, which will be not capable in capturing a fluxon. The long axis of the smaller nanodroplet would be smaller than 300 nm. The distance between two Ga nanodroplets should be larger than magnetic penetration length λ (about 10 nm) but smaller than the coherence length ξ (about 40 nm) of EGaIn. Thus, we estimate it to be ∼40 nm. The magnetic field from the trapped fluxons can be simply estimated by fluxon number divided by the area of the smaller Ga nanodroplet, which gives ∼600 Oe for one
Figure 5. Measurement-history-dependent Tc−Hc phase diagram summarizing Figure 4. The orange line coincides with the Tc of a pure Ga nanowire in a zero field, and the green line corresponds to the Tc of a Ga nanodroplet in the presence of magnetic field (see text for further elaboration). The black solid line shows Hc1 as a function of T of the EGaIn. When H < Hc1, the EGaIn is in the Meissner state. When Hc1 < H < Hc2, EGaIn is still superconducting, but fluxes can freely tunnel in the wire. Black dashed lines schematically separate regions of H that would capture different numbers of fluxons (not measured). Paths a, b, c, and d show four different measurement scan paths where we begin by cooling from 8 K under zero H. Blue and red colors represent zero and 60 Ω (or higher) resistance states, respectively. R switching between zero and 60 Ω are found in paths a, b, and c. By not crossing Hc1, R stays zero along path d.
Figure 6. A model with two neighboring Ga nanodroplets that is consistent with all the experimental observations. The different microscopic states of the two neighboring Ga nanodroplets controlling the zero and 60 Ω states of the nanowire as shown in regions I (low field) and II (intermediate field) of Figure 5. Each arrow depicts a fluxon. Superconducting and normal regions are shown, respectively, in blue and red. The region of direct/inverse proximity effect between normal Ga nanodroplets and superconducting EGaIn shell is shown by gradient color between blue and red. The smaller Ga nanodroplet is surrounded by a sufficiently thick EGaIn shell that makes it possible to trap 1 or 2 fluxons when EGaIn is superconducting. The diameter of the larger Ga limits the thickness of the surrounding EGaIn and prevents the trapping of even 1 fluxon. When the larger Ga nanodroplet is superconducting, the nanowire shows zero resistance. The 60 Ω state appears when the larger Ga nanodroplet is driven normal by one trapped fluxon with additional external magnetic field in region II or by two trapped fluxons in the smaller nanodroplet in both regions I and II. The regions I and II are defined in the phase diagram of Figure 5. The 60 Ω state is contributed jointly by the Ga nanodroplet and the surrounding EGaIn and the interface resistance between the Ga nanodroplet and the superconducting EGaIn.
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trapped fluxon and ∼1200 Oe for two trapped fluxons. An essential question is whether the surrounding EGaIn around the smaller nanodroplets can trap two magnetic fluxons. To answer this question, we consider a related geometry of a thin superconducting ring to model the state in which the EGaIn is superconducting but the (smaller) Ga nanodroplet is normal. The maximum number of trapped fluxons in this geometry has been studied.23 From the London equation, ∇ × (λ2μ0j + A) = nfluxΦ0, where λ is the penetration length, μ0 is magnetic permeability, j is supercurrents, A is vector potential, nflux is the fluxon number, and Φ0 is flux quanta. The maximum number of trapped fluxons is limited by the condition that the induced circulating currents are less than the critical current of the superconductor, namely, EGaIn. This number is given by n max =
nanowire, and R vs H scans showing the hysteretic resistance switching behaviors for different samples. This material is available free of charge via the Internet at http://pubs.acs.org.
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Corresponding Authors
*E-mail: [email protected] (W.Z.). *E-mail: [email protected] (M.H.W.C.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
We thank Nitin Samarth, D. H. Lee, Justin Sparks, Meenakshi Singh, James Kally, and Jue Jiang for helpful discussions. This work is supported by the Penn State Materials Research Science and Engineering Center, funded by the National Science Foundation under grants DMR 0820404 and DMR 1420620. Work at the Advanced Photon Source (APS) and the Center for Nanoscale Materials at APS was supported by the U.S. Department of Energy under Contract DE-AC0206CH11357. We thank Dr. Volker Rose for technical assistance at APS Beamline 26-ID-C. T.C.F.’s work at the APS was supported by the Energy Frontier Research in Extreme Environments (EFree) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE) under Award DE-SC0001057. We acknowledge partial support for X.L. by the DOE under Grant Number DE-SC0005042.
3/2 2 ravg
3ξ 3λ
where the radius ravg is about 100 nm in our samples, and the coherence length ξ is about 40 nm for EGaIn. Since at least one fluxon can be trapped inside the nanodroplet, the penetration depth cannot be larger than the smallest thickness of the EGaIn wall surrounding the relevant Ga nanodroplet. Therefore, with λ ≈ 10 nm, we obtain nmax ≈ 2, which is consistent with our physical explanation above. Prospects. We note that the quasi-1D geometry is crucial for this purpose; in two or three dimensions, the trapping or expulsion of a single fluxon does not cause a macroscopic step change in the resistance. The long length of the nanowires is also important for this experiment because the effect depends on a relatively rare configuration of a pair of Ga nanodroplets in close proximity. Measurements were carried out on a total of 11 GaIn wires, and evidence of sharp hysteretic switching between two metastable states in magnetoresistance scans similar to that reported here were seen in four wires (Supporting Information, Figure S4). This experiment can be viewed as a nanorealization of a previously proposed Josephson memory element24 that can store and retrieve binary data in a nondestructive manner. It suggests it is feasible to develop nanoscale single fluxon devices in a controllable manner, such as an addressable logic and memory device fabricated by means of e-beam nanolithography in which the “peas in a pod” configuration of two superconducting materials with different Tc and Hc. Future experiments in that direction, especially to determine the most optimal configurations, are being planned. Summary and Conclusion. In conclusion, we have demonstrated that the macroscopic resistance of a nanowire can switch between zero and nonzero values by addition or removal of a single fluxon. This behavior relies on the “peas in a pod”configuration of the nanowire, which consists of superconducting Ga−In eutectic with spontaneously formed Ga nanodroplets along the length of the nanowire. A large enough Ga nanodroplet can create a Josephson weak-link, which can be driven to a resistive state by a nearby smaller Ga nanodroplet that traps one or more superconducting fluxons. This experiment suggests possible realization of nanoscale single fluxon devices.
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AUTHOR INFORMATION
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ASSOCIATED CONTENT
S Supporting Information *
Pressure assisted melt filling technique to make centimeter-long nanowires, R vs H scans under different currents, R vs T scans under fixed H during the warming process for the Ga−In 157
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(15) Lee, H. W.; Schmidt, M. A.; Russell, R. F.; Joly, N. Y.; Tyagi, H. K.; Uebel, P.; Russell, P. S. J. Opt. Express 2011, 19 (13), 12180− 12189. (16) Sazio, P. J. A.; Amezcua-Correa, A.; Finlayson, C. E.; Hayes, J. R.; Scheidemantel, T. J.; Baril, N. F.; Jackson, B. R.; Won, D. J.; Zhang, F.; Margine, E. R.; Gopalan, V.; Crespi, V. H.; Badding, J. V. Science 2006, 311 (5767), 1583−1586. (17) Healy, N.; Lagonigro, L.; Sparks, J. R.; Boden, S.; Sazio, P. J. A.; Badding, J. V.; Peacock, A. C. Opt. Lett. 2011, 36 (13), 2480−2482. (18) Gregory, W. D.; Sheahen, T. P.; Cochran, J. F. Phys. Rev. 1966, 150 (1), 315. (19) Svirbely, W. J.; Selis, S. M. J. Phys. Chem. 1954, 58 (1), 33−35. (20) Chen, X. M.; Fei, G. T.; Li, X. F.; Zheng, K.; Zhang, L. D. J. Phys. Chem. Solids 2010, 71 (6), 918−921. (21) Winarski, R. P.; Holt, M. V.; Rose, V.; Fuesz, P.; Carbaugh, D.; Benson, C.; Shu, D. M.; Kline, D.; Stephenson, G. B.; McNulty, I.; Maser, J. J. Synchrotron Radiat. 2012, 19, 1056−1060. (22) Skocpol, W. J.; Beasley, M. R.; Tinkham, M. J. Low Temp. Phys. 1974, 16 (1−2), 145−167. (23) Denisov, D. V.; Shantsev, D. V.; Galperin, Y. M.; Johansen, T. H. 2007, arXiv:cond-mat/0709.1086. arXiv.org e-Print archive. http:// arxiv.org/abs/0709.1086. (24) Kadin, A. M. Introduction to Superconducting Circuits; John Wiley & Sons, Inc.: New York, 1999; Chapter 6.
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Single-Fluxon Controlled Resistance Switching in Centimeter-Long Superconducting Gallium−Indium Eutectic Nanowires Weiwei Zhao,*,†,‡ Jesse L. Bischof,†,¶ Jimmy Hutasoit,†,‡ Xin Liu,†,‡ Thomas C. Fitzgibbons,†,¶ John R. Hayes,§ Pier J.A. Sazio,§ Chaoxing Liu,†,‡ Jainendra K. Jain,†,‡ John V. Badding,†,¶ and M. H. W. Chan*,†,‡ †
Center for Nanoscale Science, Pennsylvania State University, University Park, Pennsylvania16802, United States Department of Physics, Pennsylvania State University, University Park, Pennsylvania16802, United States ¶ Department of Chemistry, Pennsylvania State University, University Park, Pennsylvania16802, United States § Optoelectronics Research Centre, University of Southampton, Highfield, Southampton SO17 1BJ, U.K. ‡
S Supporting Information *
ABSTRACT: The ability to manipulate a single quantum object, such as a single electron or a single spin, to induce a change in a macroscopic observable lies at the heart of nanodevices of the future. We report an experiment wherein a single superconducting flux quantum, or a fluxon, can be exploited to switch the resistance of a nanowire between two discrete values. The experimental geometry consists of centimeter-long nanowires of superconducting Ga−In eutectic, with spontaneously formed Ga nanodroplets along the length of the nanowire. The nonzero resistance occurs when a Ga nanodroplet traps one or more superconducting fluxons, thereby driving a Josephson weak-link created by a second nearby Ga nanodroplet normal. The fluxons can be inserted or flipped by careful manipulation of the magnetic field or temperature to produce one of many metastable states of the system. KEYWORDS: GaIn, eutectic, superconducting nanowire, single flux quantum, resistance switching
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typical length of 20 cm. The liquid metal wires stay inside the fiber even after the pressure is removed. The inner diameter of these fibers is uniform to a few nanometers along the entire length as measured by cross sectional scanning electron micrograph. They have a surface roughness on the order of ±0.1 nm RMS.16,17 After the infiltration, both ends of a 6 mm segment of the fiber were immersed into ∼1 mm diameter reservoirs of Ga or Ga−In and then electrically connected by 100 μm diameter Au wires for four leads transport measurements (Figure 1c). As shown in Figure 1d, a pure Ga wire shows a superconducting transition at 1.1 K, same as the bulk value.18 The room temperature resistivity value of pure Ga wire is 1.6 times the bulk value. This indicates that the nanowires inside the glass fiber are of higher quality than those fabricated by ebeam assisted evaporation and also those grown by electrodeposition in track-etched membrane. Ga−In nanowires with Ga concentration slightly higher than the eutectic point (75% Ga by weight) show two resistance steps (Figure 1e), the first from 11 kΩ to 60 Ω between 3.5 and 5 K and the second to zero resistance more sharply at 1.1 K. This can be understood
odern techniques have made it possible to observe a dramatic modulation of resistance induced by the addition of a single electron into a quantum dot, such as a single electron transistor.1−6 Recent experiments have shown that it is also possible to detect electrical signatures due to a change in the state of a single electron spin in a variety of physical systems.7−11 Single flux quantum sensitivity has also been observed in superconducting loop devices based on Josephson junctions.12,13 However, the size of the unit based on this structure is still larger than tens of micrometer.14 We report here on switching between a superconducting and a resistive state by the addition of a single magnetic flux quantum in sub150 nm geometry. This is made possible by the availability of centimeter-long superconducting Ga−In nanowires with multiple Ga nanodroplets residing along the length. This “peas in a pod” configuration of two superconducting materials with different transition temperatures and critical fields is crucial for this purpose; the normal Ga nanodroplets surrounded by superconducting Ga−In alloy in 150 nm diameter wire are natural locations where fluxons can be trapped. “Peas in a Pod” Configuration of the GaIn Nanowires. The nanowires studied in this experiment were fabricated by means of modified high pressure infiltration15 (Supporting Information, Figure S1) of molten liquid Ga or Ga−In into hollow silica fiber of 150 nm inner diameter (Figure 1a,b) and © 2014 American Chemical Society
Received: August 26, 2014 Revised: November 3, 2014 Published: November 26, 2014 153
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Figure 1. Ga and Ga−In nanowires of 150 nm diameter and 6 mm length. (a) An optical image of the glass fiber infiltrated with Ga. (b) An end view of a hollow fiber by field emission scanning electron microscopy. (c) The schematic for four probe transport measurements. (d) Resistance as a function of temperature (R vs T) at zero field of a pure Ga nanowire showing a superconducting transition at 1.1 K, the bulk Tc value. The room temperature resistivity is 45.3 μΩ·cm, 1.6 times the bulk value. The inset shows a warming−cooling hysteresis loop, indicating that Ga inside the fiber freezes at 250 K instead of 303 K, the bulk freezing point. (e) R vs T at zero field for a Ga−In nanowire with Ga concentration slightly above the eutectic concentration (75% Ga by weight). A two stage superconducting transition at 3.5−5 and 1.1 K is found. Warming and cooling hysteresis similar to that of pure Ga is also found. (f) A two-dimensional X-ray fluorescence map at 190 K of the Ga−In nanowire, showing two droplets in close proximity with high Ga concentration surrounded by Ga−In eutectic (EGaIn). The spatial resolution is 25 nm. The excitation current used here, unless specified otherwise, is 5 nA.
Figure 2. Voltage−current (V−I) scans for the Ga−In nanowire. (a) V vs I under different H at T = 0.5 K. (b) V vs I at different T under zero field. V−I measurements show many steps in V. The steps are signatures of critical currents in the nanowire. These different critical currents indicate that there are multiple Ga droplets of different diameters and hence different thicknesses of the surrounding Ga−In eutectic shell or weak links in the nanowire.
Figure 3. Magnetoresistance of the Ga−In nanowire. (a) The magnetoresistance results are qualitatively different below and above Tc = 1.1 K. At T = 1.2 K, the magnetoresistance results show that resistance (R) stays constant at 60 Ω at low field and increases with magnetic field (H) for H > 500 Oe, which plateaus to the normal state value of 11 kΩ. The magnetoresistance at 0.5 K shows a two-step transition. A sharp transition occurs at a specific value 490 Oe, which we designated as Hc1, and then there is a gradual increase in resistance toward the normal state value with increasing magnetic field. There is no well-defined critical field for the second transition. For specificity, we choose Hc2 as the field value where resistance of the nanowire is 90% of the normal state value. Between Hc1 and Hc2 the EGaIn is in the mixed state. (b) Hc2 as a function of temperature (T). Beyond Hc2(T), the EGaIn is normal.
in terms of phase separation into two regions;19,20 one is pure Ga with a lower superconducting transition (Tc) at 1.1 K, and the other is Ga−In eutectic (EGaIn) with a higher superconducting transition (Tc′) between 3.5 and 5 K. We have directly confirmed that the phase separated residual Ga forms nanodroplets surrounded by EGaIn by X-ray fluorescence (XRF) spectroscopy21 (Figure 1f). The Ga nanodroplets are likely to be of different sizes, residing randomly along the nanowire like peas in a pod. If all Ga nanodroplets were very small, the resistance of the nanowire would remain zero so long as EGaIn is superconducting, independent of whether the Ga nanodroplets are normal or superconducting. We assign the 60 Ω resistance to a relatively large normal Ga nanodroplet with very thin EGaIn layer, which is driven normal by the excitation current of 5 nA. This assignment is confirmed by voltage− current measurements (Figure 2) that show many steps in
voltage with increasing current suggesting the presence of multiple Ga nanodroplets with different diameters and surrounded by EGaIn shells of different thicknesses with different critical currents,22 which range from nanoamps to tens of microamps in this work. The critical magnetic fields at which vortices can tunnel through the EGaIn shells also depend on the thickness of the EGaIn shells for a fixed excitation current; this is confirmed by R vs H scanning at fixed current (Supporting Information, Figure S2). 154
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Figure 4. Resistance (R) as a function of magnetic field (H) and temperature (T) for the Ga−In nanowire, obtained by two different scan paths of R vs H at fixed T and R vs T at fixed H. All measurement scans began by cooling the sample from 8 K under zero H to 0.5 K. (a−c) Magnetoresistance measurements with the field perpendicular to the nanowire at 0.5, 1.0, and 1.2 K. (d) R vs T scans at 0 Oe. (e, f) R vs T scans under 200 Oe when the maximum temperature is 2 K (e) and 8 K (f). (g) Three dimensional (3D) R(T,H) by H scanning at fixed T. (h) 3D R(T,H) by T scanning at fixed H. The warming−cooling process starts from 0.5 K, warms to 8 K, and cools to 0.5 K.
The same Tc is found when the wire is cooled under zero field (Figure 4d) irrespective of the maximum temperature reached in the warming cycle. Similarly, no hysteresis is seen in cycle under 200 Oe if the maximum temperature is 2 K (Figure 4e). However, if the maximum temperature is increased to 8 K in the cycle, then Tc is suppressed to 0.8 K during cooling when placed under the same 200 Oe (Figure 4f). A more complete view of the hysteretic behaviors as a function of H and T plots is shown in Figure 4g,h, respectively. Figure 5 summarizes the hysteretic behavior in both H and T scans. No hysteretic behavior is seen if the measurement path, such as paths a and d, is kept inside of the black solid line, which is Hc1(T) of EGaIn, the phase boundary separating the Meissner state and the mixed state. We define this zero resistance state obtained at the end of paths a or d as state A. Hysteretic behaviors happen when the black line is crossed during the measurement, paths b and c. Although both paths b and c end at the same low field and low temperature region, different resistance, namely, zero and 60 Ω, respectively, are found. This indicates that these paths lead to different final states B and C.
Hysteretic Resistance Switching Behaviors. The qualitative difference in the magnetoresistance below and above Tc = 1.1 K is striking (Figure 3). When the temperature (T) is 1.2 K, the magnetoresistance stays constant at 60 Ω at low fields and increases with magnetic field (H) for H > 500 Oe, which plateaus to the normal state value of 11 kΩ near 2800 Oe, which we will call Hc2. Beyond Hc2, the GaIn wire becomes normal. The magnetoresistance below 1.1 K (Figure 4a,b) shows hysteretic switching between zero and 60 Ω. When H is increased to a specific value, which we designate as Hc1, the resistance (R) abruptly jumps from zero to 60 Ω and stays at this value even when H is reverted to zero. When H reaches a negative specific field (−Hc1′) (|Hc1′| < |Hc1|), R drops back to zero. R jumps to 60 Ω again when H reaches −Hc1. After H reverts to positive direction, R will follow a symmetric loop. At T = 1.2 K > Tc, no hysteresis shows up in the magnetoresistance results (Figure 4c). Hysteretic behavior was also seen in R vs T scans when the wire was subjected to warming− cooling cycles at fixed H provided the maximum temperature exceeded a certain value. During the warming process, the superconducting transition (to 60 Ω) is found at 1.1 K for all field values below 330 Oe (Supporting Information, Figure S3). 155
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Fluxon Trapping Model. The hysteretic resistance switching behaviors and the three different history dependent states can be understood by a fluxon trapping model. As noted above, normal Ga nanodroplets are natural locations where fluxons can be trapped. In particular, once a fluxon going through a relatively small Ga nanodroplet is trapped, it cannot leak out so long as the surrounding EGaIn is superconducting. However, trapped fluxons cannot cause any resistance. The simplest model that can exhibit both trapped fluxons and a nonzero resistance is that of two Ga nanodroplets of different sizes in close proximity, as shown in Figure 6. We identify the states A, B, and C as the states with zero, one, and two fluxons trapped in the smaller Ga nanodroplet, respectively. The thin EGaIn layer surrounding the larger nanodroplet behaves like a weak link not capable of capturing a fluxon, and the 60 Ω resistance appears when the larger Ga nanodroplet becomes normal. This is the case when the temperature is raised above the orange line in path a in Figure 5. The orange line is independent of external field at 1.1 K because the Ga droplets “see” zero field due to the Meissner effect of the GaIn shell. The Meissner effect also assures that no fluxon is captured by the smaller Ga nanodroplet. Along path “b”, when the black line is crossed from high to low temperatures, a single fluxon is trapped by the smaller Ga nanodroplet. As a result of the magnetic field due to the circulating currents supporting this fluxon, it is necessary to go to a lower T (green line in Figure 5) before the nearby larger Ga nanodroplet becomes superconducting (The green line separates the superconducting and normal phases of the larger Ga nanodroplet in the presence of the magnetic field due to a single trapped fluxon in the smaller nanodroplet and the external field). Finally, along the path c, when the black line is crossed at a much higher magnetic field than that in the path b, two fluxons are trapped in the smaller nanodroplet. The circulating current is now so large that it drives the larger nanodroplet normal even at a zero external H and the lowest T (0.5 K in our study). This explains how a state with nonzero resistance can be stable even under a zero external H (state C): the stability comes from the trapping of fluxons in the smaller Ga nanodroplet while the resistance comes from the larger one. We note that the number of trapped fluxons depends on the external H; we have schematically depicted the regions that trap zero, one, and two fluxons by dashed lines in the phase diagram of Figure 5. This model is qualitatively consistent with all the observations. It is not possible to make the model quantitative, given the lack of detailed and precise information about the configuration of the Ga nanodroplet pair. However, semiquantitative statements can be made regarding the plausibility of the above model of fluxon trapping. According to the XRF results, the Ga nanodroplets are of elliptical shape with dimensions ranging from tens to hundreds of nanometers. It is reasonable to infer that when the long axis of the larger elliptical Ga nanodroplet reaches ∼300 nm, its width would be close to 150 nm, the diameter of the nanowire, with the surrounding EGaIn shell forming a weak link, which will be not capable in capturing a fluxon. The long axis of the smaller nanodroplet would be smaller than 300 nm. The distance between two Ga nanodroplets should be larger than magnetic penetration length λ (about 10 nm) but smaller than the coherence length ξ (about 40 nm) of EGaIn. Thus, we estimate it to be ∼40 nm. The magnetic field from the trapped fluxons can be simply estimated by fluxon number divided by the area of the smaller Ga nanodroplet, which gives ∼600 Oe for one
Figure 5. Measurement-history-dependent Tc−Hc phase diagram summarizing Figure 4. The orange line coincides with the Tc of a pure Ga nanowire in a zero field, and the green line corresponds to the Tc of a Ga nanodroplet in the presence of magnetic field (see text for further elaboration). The black solid line shows Hc1 as a function of T of the EGaIn. When H < Hc1, the EGaIn is in the Meissner state. When Hc1 < H < Hc2, EGaIn is still superconducting, but fluxes can freely tunnel in the wire. Black dashed lines schematically separate regions of H that would capture different numbers of fluxons (not measured). Paths a, b, c, and d show four different measurement scan paths where we begin by cooling from 8 K under zero H. Blue and red colors represent zero and 60 Ω (or higher) resistance states, respectively. R switching between zero and 60 Ω are found in paths a, b, and c. By not crossing Hc1, R stays zero along path d.
Figure 6. A model with two neighboring Ga nanodroplets that is consistent with all the experimental observations. The different microscopic states of the two neighboring Ga nanodroplets controlling the zero and 60 Ω states of the nanowire as shown in regions I (low field) and II (intermediate field) of Figure 5. Each arrow depicts a fluxon. Superconducting and normal regions are shown, respectively, in blue and red. The region of direct/inverse proximity effect between normal Ga nanodroplets and superconducting EGaIn shell is shown by gradient color between blue and red. The smaller Ga nanodroplet is surrounded by a sufficiently thick EGaIn shell that makes it possible to trap 1 or 2 fluxons when EGaIn is superconducting. The diameter of the larger Ga limits the thickness of the surrounding EGaIn and prevents the trapping of even 1 fluxon. When the larger Ga nanodroplet is superconducting, the nanowire shows zero resistance. The 60 Ω state appears when the larger Ga nanodroplet is driven normal by one trapped fluxon with additional external magnetic field in region II or by two trapped fluxons in the smaller nanodroplet in both regions I and II. The regions I and II are defined in the phase diagram of Figure 5. The 60 Ω state is contributed jointly by the Ga nanodroplet and the surrounding EGaIn and the interface resistance between the Ga nanodroplet and the superconducting EGaIn.
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trapped fluxon and ∼1200 Oe for two trapped fluxons. An essential question is whether the surrounding EGaIn around the smaller nanodroplets can trap two magnetic fluxons. To answer this question, we consider a related geometry of a thin superconducting ring to model the state in which the EGaIn is superconducting but the (smaller) Ga nanodroplet is normal. The maximum number of trapped fluxons in this geometry has been studied.23 From the London equation, ∇ × (λ2μ0j + A) = nfluxΦ0, where λ is the penetration length, μ0 is magnetic permeability, j is supercurrents, A is vector potential, nflux is the fluxon number, and Φ0 is flux quanta. The maximum number of trapped fluxons is limited by the condition that the induced circulating currents are less than the critical current of the superconductor, namely, EGaIn. This number is given by n max =
nanowire, and R vs H scans showing the hysteretic resistance switching behaviors for different samples. This material is available free of charge via the Internet at http://pubs.acs.org.
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Corresponding Authors
*E-mail: [email protected] (W.Z.). *E-mail: [email protected] (M.H.W.C.). Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
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REFERENCES
We thank Nitin Samarth, D. H. Lee, Justin Sparks, Meenakshi Singh, James Kally, and Jue Jiang for helpful discussions. This work is supported by the Penn State Materials Research Science and Engineering Center, funded by the National Science Foundation under grants DMR 0820404 and DMR 1420620. Work at the Advanced Photon Source (APS) and the Center for Nanoscale Materials at APS was supported by the U.S. Department of Energy under Contract DE-AC0206CH11357. We thank Dr. Volker Rose for technical assistance at APS Beamline 26-ID-C. T.C.F.’s work at the APS was supported by the Energy Frontier Research in Extreme Environments (EFree) Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE) under Award DE-SC0001057. We acknowledge partial support for X.L. by the DOE under Grant Number DE-SC0005042.
3/2 2 ravg
3ξ 3λ
where the radius ravg is about 100 nm in our samples, and the coherence length ξ is about 40 nm for EGaIn. Since at least one fluxon can be trapped inside the nanodroplet, the penetration depth cannot be larger than the smallest thickness of the EGaIn wall surrounding the relevant Ga nanodroplet. Therefore, with λ ≈ 10 nm, we obtain nmax ≈ 2, which is consistent with our physical explanation above. Prospects. We note that the quasi-1D geometry is crucial for this purpose; in two or three dimensions, the trapping or expulsion of a single fluxon does not cause a macroscopic step change in the resistance. The long length of the nanowires is also important for this experiment because the effect depends on a relatively rare configuration of a pair of Ga nanodroplets in close proximity. Measurements were carried out on a total of 11 GaIn wires, and evidence of sharp hysteretic switching between two metastable states in magnetoresistance scans similar to that reported here were seen in four wires (Supporting Information, Figure S4). This experiment can be viewed as a nanorealization of a previously proposed Josephson memory element24 that can store and retrieve binary data in a nondestructive manner. It suggests it is feasible to develop nanoscale single fluxon devices in a controllable manner, such as an addressable logic and memory device fabricated by means of e-beam nanolithography in which the “peas in a pod” configuration of two superconducting materials with different Tc and Hc. Future experiments in that direction, especially to determine the most optimal configurations, are being planned. Summary and Conclusion. In conclusion, we have demonstrated that the macroscopic resistance of a nanowire can switch between zero and nonzero values by addition or removal of a single fluxon. This behavior relies on the “peas in a pod”configuration of the nanowire, which consists of superconducting Ga−In eutectic with spontaneously formed Ga nanodroplets along the length of the nanowire. A large enough Ga nanodroplet can create a Josephson weak-link, which can be driven to a resistive state by a nearby smaller Ga nanodroplet that traps one or more superconducting fluxons. This experiment suggests possible realization of nanoscale single fluxon devices.
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AUTHOR INFORMATION
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ASSOCIATED CONTENT
S Supporting Information *
Pressure assisted melt filling technique to make centimeter-long nanowires, R vs H scans under different currents, R vs T scans under fixed H during the warming process for the Ga−In 157
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